NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Seasonal Indices and Deseasonalising Data

From the beginning of 2016, the number of new houses built in the suburb of Woodford was recorded and figures are released every four months.

The following table contains the data from the beginning of 2016 to the end of 2019:

Time Period |
Houses built |
Percentage of yearly mean |

April 2016 | $6$6 | $60%$60% |

August 2016 | $21$21 | $x$x |

December 2016 | $3$3 | $30%$30% |

April 2017 | $11$11 | $y$y |

August 2017 | $24$24 | $180%$180% |

December 2017 | $5$5 | $37.5%$37.5% |

April 2018 | $15$15 | $84.91%$84.91% |

August 2018 | $25$25 | $141.51%$141.51% |

December 2018 | $13$13 | $z$z |

April 2019 | $15$15 | $77.59%$77.59% |

August 2019 | $28$28 | $144.83%$144.83% |

December 2019 | $15$15 | $77.59%$77.59% |

a

For 2016, 2017 and 2018, calculate the mean number of houses built in each time period.

Give your answers to two decimal places.

Year | 2016 | 2017 | 2018 |

Mean | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Use your answers from part (a) to calculate the value of $x$`x`.

Give your answer to two decimal places.

c

Use your answers from part (a) to calculate the value of $y$`y`.

Give your answer to two decimal places.

d

Use your answers from part (a) to calculate the value of $z$`z`.

Give your answer to two decimal places.

Easy

Approx 6 minutes

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Carry out investigations of phenomena, using the statistical enquiry cycle: A conducting experiments using experimental design principles, conducting surveys, and using existing data sets B finding, using, and assessing appropriate models (including linear regression for bivariate data and additive models for time-series data), seeking explanations, and making predictions C using informed contextual knowledge, exploratory data analysis, and statistical inference D communicating findings and evaluating all stages of the cycle.

Investigate time series data